Bayesian Model Selection

Three sided coin

Model 1: Surface Area

\[p(h, R) = \frac{2\pi R h}{2\pi R^2 + 2\pi Rh}\]

\[p(\eta) = \frac{\eta}{1 + \eta}\]

Model 2: Cross-sectional Length

\[ p(h, R) = \frac{h}{2(2R) + h}\] \[ p(\eta) = \frac{\eta}{4 + \eta} \]

Model 3: Cross-sectional angle

Model 3: Cross-sectional angle

Model 3: Cross-sectional angle

\[ p(\eta) = \frac{\arctan (\eta/2)}{\arctan(\eta/2) + \arctan(2/\eta)} \]

Model 4: Spherical Surface Area

\[ p(\eta) = \,? \]

MCMC: Gibbs Sampling

Changepoint problem